The empirical correlation between the mass of a super-massive black hole ( \mathcal { M } _ { BH } ) and its host galaxy properties is widely considered to be evidence of their co-evolution .
A powerful way to test the co-evolution scenario and learn about the feedback processes linking galaxies and nuclear activity is to measure these correlations as a function of redshift .
Unfortunately , currently \mathcal { M } _ { BH } can only be estimated in active galaxies at cosmological distances .
At these distances , bright active galactic nuclei ( AGN ) can outshine the host galaxy , making it extremely difficult to measure the host ’ s luminosity .
Strongly lensed AGNs provide in principle a great opportunity to improve the sensitivity and accuracy of the host galaxy luminosity measurements as the host galaxy is magnified and more easily separated from the point source , provided the lens model is sufficiently accurate .
In order to measure the \mathcal { M } _ { BH } - L correlation with strong lensing , it is necessary to ensure that the lens modelling is accurate , and that the host galaxy luminosity can be recovered to at least a precision and accuracy better than that of the typical \mathcal { M } _ { BH } measurement .
We carry out extensive and realistic simulations of deep Hubble Space Telescope observations of lensed AGNs obtained by our collaboration .
We show that the host galaxy luminosity can be recovered with better accuracy and precision than the typical uncertainty on \mathcal { M } _ { BH } ( \sim 0.5 dex ) for hosts as faint as 2 - 4 magnitudes dimmer than the AGN itself .
Our simulations will be used to estimate bias and uncertainties on the actual measurements to be presented in a future paper .